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From these illustrations we derive the following

RULE.
Q. How do you obtain the numerator ?

A. Bring the given denominations to the lowest denomination mentioned, for a numerator.

Q. How do you obtain the denominator ?

A. Bring 1 (or an integer) of that higher denomination into the same denomination, for a denominator.

More Exercises for the Slate. 2. What part of 1 £. is 2 s. 6 d.

A. = 3. What part of 1 hundred weight is 3 qrs. 15 lbs. 14 oz. ?

A. 398 4. What part of 1 vard is 3 qrs. 3 na. ?. A. tá 5. What part of 1 bushel is 3 pecks, 7 qts. 1 pt. ?**

A. 6. What part of 1 tun is 1 gallon, 0 qts. 2 pts. 1 gill?

A. gota 7. What part of 15 pipes is 25 galls. ?

A. g. 8. What part of 2 miles is 7 fur. 11 in. 2 b. c. ?

A. 78332 9. What part of 1 month is 19 days ?

A. 38. 10. What part of 1 month is 25 days, 13 hours ?

A. 918 11. What part of 1 month is 22 days, 15 h. 1 min.?"

9 XLIX. TO REDUCE A FRACTION TO WHOLE Num

BERS OF LESS DENOMINATIONS, OR, TO FIND THE VALUE OF A FRACTION. 1. How much is of a shilling? How much It of a lb.'

of a lb.? Hoe of a lb. ? it of a lb.? 14 of a Ib.; end of 1 qr. of a cwt. ? ? g? 18? 37? 1 an hour! ? *?

Operation by Slate illustrated. 1 What is the value of of a pound ?

OPERATION.

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Q. How do you proNumer. 5

ceed in this example?

and why? 20 s.

A. Aš 1 £. = 205, Denom. 6)100(16 s. of one pound is iše

same as of 20 s., 711], to get of 20, we in iltiply the numerator 5 and 20 together, mak

ing 100; which, divid 16 s. 8 d. Ans. 4

ed by the denominator 12

6, gives 16 s. and of

another shilling re48 (8 d.

maining. This = 48

of 12 d.; then, of

12 d.=8 d.
From these illustrations we derive the following

RULE.
Q. What do you multiply the numerator by ?

A. By as many of the next denomination as make one of that; that is, pounds by what makes a pound, ounces by what makes an ounce, as in Reduction of whole numbers.

Q. What do you divide the product by ?
A. By the denominator.
Q. If there be a remainder, how do you proceed ?
A. Multiply and divide as before.

More Exercises for the Slate.
2. What is the value of of a cwt. ? A. 3 qrs.
3. What is the value of į of an acre ? A. 1 rood, 13} rds.

4. What is the value of any of a pound Troy? A. 10 oz. $ pwts. 167.

5. What is the value of 243 of a hogshead ? A. 49 gallony 12922 qts.

6. What is the value of 371 of a pound avoirdupois? A. 1 lb 1437 i oz.

7. What is the value of 30 of a hogshead? A. 50 gallons.

8. What is the value of 13 of a day? A. 16 hours, 36 min 56 sec.

IL, TO REDUCE FRACTIONS OF A HIGHER DENOMINA

TION INTO A LOWER. We have seen (1T XXXVIII.) that fractions are multiplied by multiplying their numerators, or dividing their denominators. 1. Reduce so £. to the fraction of a penny.

1 In this example, we multi OPERATION.

ply the 1, in ato, as in Re Numer. 1

duction of whole numbers 20 s.

viz., pounds by what makes a

pound, shillings by what 20

makes a shilling, &c. But 12 d.

this operation may be express

ed differently, thus ; 450 X New numer. 240

20 x 12= 48= d.; or, by

dividing the denominators, Then, 240

thus; 20020=24:12= =fd. Ans. Denom. 4801

. 1 d., Ans., as before, in its

est terms.

RULE.
Q. How, then, would you proceed ?

A. Multiply the fraction, as in Reduction ut whole numbers.

More Exercises for the Slate. 2. Reduce zło of a pound to the fraction of a shilling.

A. The 3. Reduce 1920 of a pound to the fraction of a farthing.

A. 4. Reduce Tots of a hogshead to the fraction of a gallon.

A. To gas 5. Reduce TýT of a bushel to the fraction of a quart.

4. Iff gt 6. Reduce 1117 of a day to the fraction of a minute.

A. 1941 m. 7. Reduce Tomg of a cwt. to the fraction of a pound.

A. & I 8. Reduce bio of a hhd. to the fraction of a pint. A. pt. 9. Reduce T&o of a pound to the fraction of a shilling.

DIKON

ILI. TO REDUCE FRACTIONS OF A LOT

TION INTO A EJCEER

We have seen, that, to & Tide a fract. II. *? En multiply the denominator, or CITde e EZ

This rule is the re rerse of the as, TL, 2RC PETE
1. Reduce of a penny to the fruction of a pound
OPERATION. 1 In this example. ve Tide as Pie
Denom. 2

duction, I IXIL, TI, PB 17
peace,
s

ty :
order fo this, we z ebet
the denominatoa 0:ė Tide the 2003
tor by the sazne pondets 32: we socket

diride br in Peduction of the num

I bers. The same result in de dotzin New denom. 480 ed if performed thus: Then, tšo, Ans. Í *x 12 x2= 5 £., Års.

Hence the following

RULE.
Q. How do you proceed?
A. Divide as in Reduction of whole numbers.

More Exercises for the Slate. 2. Reduce 1 of a shilling to the fraction of a pound.

4. zo £. 3. Reduce 1 of a farthing to the fraction of a pound.

A. 1920 £. 4. Reduce It of a gallon to the fraction of a hogshead.

A. Tobg hhd. 5. Reduce 144 of a quart to the fraction of a bushel.

A. bu. 6. Reduce 1411 of a minute to the fraction of a day.

A. TALT: 9. Reduce ☆ of a pound to the fraction of a hundred weight.

A. Toor 8. Reduce of a pint to the fraction of a hogshead.

A. 2520 =oto. 9. Reduce of a shilling to the fraction of a pound.

A. O

DECIMAL FRACTIONS. 9 LII. Q. When such fractions as these occur, viz. So, ifra 73 , how is a unit supposed to be divided ?

A. Into 10 equal parts, called tenths; and each tenth into 10 other equal parts, called hundredths, and each hundredth into 10 more equal parts, called thousandths, &c.

Q. How is it customary to write such expressions ?

A. By taking away the denominator, and placing a comma before the numerator.

Let me see you write down, in this manner, or, too, ooo

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Q. What name do you give to fractions written in this manner ?
A. Decimal Fractions.
Q. Why called decimal ?

A. From the Latin word decem, signifying ten; because they increase and decrease in a tenfold proportion, like whole numbers.

Q. What are all other fractions called ?
A. Vulgar, or Common Fractions.

Q. In whole numbers, we are accustomed to call the right-hand figure, units, from which we begin to reckon no cumerate; hence it was found convenient to make the swille piace a starting point in decimals, and to do this, we make use of a comma; what, then, is the use of this comma ?

A. It merely shows where the units' place is.
Q. What are the figures on the left of the comma called?
A. Whole numbers.
Q. What are the figures on the right of the comma called ?
A. Decimals.
Q. What, then, may the comma properly be called ?
A. Separatrix.
Q. Why?

A. Because it separates the decimals from the whole numbers.

Q. What is the first figure at the right of the separatrix called ?
A. 10ths.
Q. What is the second, third, fourth, &c. ?
A. The second is hundredths, the third thou.

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